I am currently working on the Coclass of Nilpotent Leibniz Algebras under Dr. Ernest Stitzinger at North Carolina State University. The coclass of a Leibniz algebra gives us important information about the structure of a Leibniz algebra, and what it's corresponding upper central series looks like. This research provides the classification of all possible Leibniz algebras, over various fields, that are coclass 0, 1, or 2. This work extends the results found in the field of Lie algebras, which was developed based on group theory. You can read more about my research, and its background, by reading my research statement.
For my master's thesis, I studied Normal p-Complement Theorems under the advisement of Dr. Thomas Wakefield at Youngstown State University. This worked considered three major theorems involving normal p-complements, including those theorems by William Burnside, Ferdinand Georg Frobenius, and John G. Thompson. You can find the final work at the link below.
As an undergraduate, I studied the Kelly Criterion under the advisement of Dr. Nathan Ritchey at Youngstown State University. Kelly's criterion is a method used for maximizing wealth in a bet. I applied the Kelly Criterion to medical malpractice and worker's compensation lawsuits in order to determine a mathematical approach of deciding when to take a legel settlement.
